MathPlotAI Logo MathPlotAI

Feynman Path Reflection Demo

Feynman Path Reflection Demo
Loading the math board and drawing, please wait…
2014-12-09 01:28
Probability & StatisticsGeometric Construction
This example demonstrates the multi-path characteristics of Feynman paths in geometric reflection. It involves core mathematical concepts like reflection, statistical characteristics, multiplication, real numbers, volume, and set theory. The construction utilizes commands and objects such as Point, Intersect, PointIn, Segment, Mirror, Midpoint, Circle, Vector, OrthogonalLine from GeoGebra. Suitable for high school and above students to understand complex geometric transformations and applications in probability & statistics.

GeoGebra Commands & Parameters

  1. Point(xAxis) → F
  2. Point(xAxis) → G
  3. Point(xAxis) → H
  4. Point(xAxis) → I
  5. Point(xAxis) → J
  6. Point(xAxis) → K
  7. Point(xAxis) → L
  8. Point(xAxis) → M
  9. Intersect(xAxis, yAxis) → N
  10. Point(xAxis) → O
  11. Point(xAxis) → P
  12. Point(xAxis) → Q
  13. Point(xAxis) → R
  14. Point(xAxis) → S
  15. Point(xAxis) → T
  16. Point(xAxis) → U
  17. Point(xAxis) → V
  18. PointIn(y ≥ 0) → D
  19. Segment(D, F) → a
  20. PointIn(y ≥ 0) → E
  21. Segment(F, E) → b
  22. Segment(D, G) → d
  23. Segment(G, E) → e
  24. Segment(D, H) → f
  25. Segment(H, E) → g
  26. Point(a) → W
  27. Point(b) → Z
  28. Mirror(A_1, yAxis) → B_1
  29. Midpoint(A_1, B_1) → C_1
  30. Midpoint(A_1, C_1) → D_1
  31. Midpoint(C_1, B_1) → E_1
  32. Midpoint(B_1, E_1) → F_1
  33. Midpoint(E_1, C_1) → G_1
  34. Midpoint(C_1, D_1) → H_1
  35. Midpoint(D_1, A_1) → I_1
  36. Midpoint(A_1, I_1) → J_1
  37. Midpoint(I_1, D_1) → K_1
  38. Midpoint(D_1, H_1) → L_1
  39. Midpoint(H_1, C_1) → M_1
  40. Midpoint(C_1, G_1) → N_1
  41. Midpoint(G_1, E_1) → O_1
  42. Midpoint(E_1, F_1) → P_1
  43. Midpoint(F_1, B_1) → Q_1
  44. Circle(A_1, 0.5) → h
  45. Circle(J_1, 0.5) → k_3
  46. Circle(I_1, 0.5) → p
  47. Circle(K_1, 0.5) → q
  48. Circle(D_1, 0.5) → r
  49. Point(h) → R_1
  50. Point(k_3) → S_1
  51. Point(p) → T_1
  52. Point(q) → U_1
  53. Point(r) → V_1
  54. Vector(A_1, R_1) → v
  55. Vector(J_1, S_1) → w
  56. Vector(I_1, T_1) → i
  57. Vector(K_1, U_1) → j
  58. Vector(D_1, V_1) → l
  59. Point(e) → W_1
  60. Point(g) → Z_1
  61. Point(d) → A_2
  62. Point(f) → B_2
  63. Circle(L_1, 0.5) → s
  64. Circle(H_1, 0.5) → t
  65. Circle(M_1, 0.5) → c_1
  66. Circle(C_1, 0.5) → d_1
  67. Circle(N_1, 0.5) → e_1
  68. Circle(G_1, 0.5) → f_1
  69. Circle(O_1, 0.5) → g_1
  70. Circle(E_1, 0.5) → h_1
  71. Circle(P_1, 0.5) → k_1
  72. Circle(F_1, 0.5) → p_1
  73. Circle(Q_1, 0.5) → q_1
  74. Circle(B_1, 0.5) → r_1
  75. Point(s) → C_2
  76. Point(t) → D_2
  77. Point(c_1) → E_2
  78. Point(d_1) → F_2
  79. Point(e_1) → G_2
  80. Point(f_1) → H_2
  81. Point(g_1) → I_2
  82. Point(h_1) → J_2
  83. Point(k_1) → K_2
  84. Point(q_1) → M_2
  85. Point(r_1) → N_2
  86. Point(p_1) → L_2
  87. Segment(D, I) → m
  88. Segment(I, E) → n
  89. Point(m) → O_2
  90. Point(n) → P_2
  91. Segment(D, J) → a_1
  92. Segment(J, E) → b_1
  93. Segment(D, K) → i_1
  94. Segment(K, E) → j_1
  95. Segment(D, L) → l_1
  96. Segment(L, E) → m_1
  97. Segment(D, M) → n_1
  98. Segment(M, E) → s_1
  99. Segment(D, N) → t_1
  100. Segment(N, E) → a_2
  101. Segment(D, O) → b_2
  102. Segment(O, E) → c_2
  103. Segment(D, P) → d_2
  104. Segment(P, E) → e_2
  105. Segment(D, Q) → f_2
  106. Segment(Q, E) → g_2
  107. Segment(D, R) → h_2
  108. Segment(R, E) → i_2
  109. Segment(D, S) → j_2
  110. Segment(S, E) → k_2
  111. Segment(D, T) → l_2
  112. Segment(T, E) → m_2
  113. Segment(D, U) → n_2
  114. Segment(U, E) → p_2
  115. Segment(D, V) → q_2
  116. Segment(V, E) → r_2
  117. Point(a_1) → Q_2
  118. Point(b_1) → R_2
  119. Point(i_1) → S_2
  120. Point(j_1) → T_2
  121. Point(l_1) → U_2
  122. Point(m_1) → V_2
  123. Point(n_1) → W_2
  124. Point(s_1) → Z_2
  125. Point(t_1) → A_3
  126. Point(a_2) → B_3
  127. Point(b_2) → C_3
  128. Point(c_2) → D_3
  129. Point(d_2) → E_3
  130. Point(e_2) → F_3
  131. Point(f_2) → G_3
  132. Point(g_2) → H_3
  133. Point(h_2) → I_3
  134. Point(i_2) → J_3
  135. Point(j_2) → K_3
  136. Point(k_2) → L_3
  137. Point(l_2) → M_3
  138. Point(m_2) → N_3
  139. Point(n_2) → O_3
  140. Point(p_2) → P_3
  141. Point(q_2) → Q_3
  142. Point(r_2) → R_3
  143. Vector(L_1, C_2) → u_1
  144. Vector(H_1, D_2) → v_1
  145. Vector(M_1, E_2) → w_1
  146. Vector(C_1, F_2) → u_2
  147. Vector(N_1, G_2) → v_2
  148. Vector(G_1, H_2) → w_2
  149. Vector(O_1, I_2) → s_2
  150. Vector(E_1, J_2) → t_2
  151. Vector(F_1, L_2) → u_3
  152. Vector(Q_1, M_2) → v_3
  153. Vector(B_1, N_2) → w_3
  154. Vector(P_1, K_2) → a_3
  155. Mirror(E, xAxis) → E'
  156. Segment(D, E') → c
  157. Intersect(c, xAxis) → A
  158. Segment(D, A) → b_3
  159. Segment(A, E) → c_3
  160. OrthogonalLine(A, xAxis) → d_3
  161. Circle(A, 6) → e_3
  162. Intersect(e_3, d_3) → C, T_3
  163. Segment(T_3, C) → f_3
  164. OrthogonalLine(A_1, xAxis) → g_3
  165. OrthogonalLine(J_1, xAxis) → h_3
  166. OrthogonalLine(I_1, xAxis) → i_3
  167. OrthogonalLine(K_1, xAxis) → j_3
  168. OrthogonalLine(D_1, xAxis) → l_3
  169. Point(yAxis) → S_3
  170. OrthogonalLine(S_3, yAxis) → m_3
  171. Point(yAxis) → U_3
  172. OrthogonalLine(U_3, yAxis) → n_3
  173. Intersect(m_3, l_3) → V_3
  174. Intersect(m_3, j_3) → W_3
  175. Intersect(m_3, i_3) → Z_3
  176. Intersect(m_3, h_3) → A_4
  177. Intersect(m_3, g_3) → B_4
  178. Intersect(n_3, l_3) → C_4
  179. Intersect(n_3, j_3) → D_4
  180. Intersect(n_3, i_3) → E_4
  181. Intersect(n_3, h_3) → F_4
  182. Intersect(n_3, g_3) → G_4
  183. Segment(G_4, B_4) → p_3
  184. Segment(F_4, A_4) → q_3
  185. Segment(E_4, Z_3) → r_3
  186. Segment(D_4, W_3) → s_3
  187. Segment(C_4, V_3) → t_3
  188. Point(p_3) → H_4
  189. Point(q_3) → I_4
  190. Point(r_3) → J_4
  191. Point(s_3) → K_4
  192. Point(t_3) → L_4
  193. Mirror(D_4, t_3) → M_4
  194. Mirror(W_3, t_3) → N_4
  195. Segment(M_4, N_4) → a_4
  196. Mirror(C_4, a_4) → O_4
  197. Mirror(V_3, a_4) → P_4
  198. Segment(O_4, P_4) → b_4
  199. Mirror(M_4, b_4) → Q_4
  200. Mirror(N_4, b_4) → R_4
  201. Segment(Q_4, R_4) → c_4
  202. Mirror(O_4, c_4) → S_4
  203. Mirror(P_4, c_4) → T_4
  204. Segment(S_4, T_4) → d_4
  205. Mirror(Q_4, d_4) → U_4
  206. Mirror(R_4, d_4) → V_4
  207. Segment(U_4, V_4) → e_4
  208. Mirror(S_4, e_4) → W_4
  209. Mirror(T_4, e_4) → Z_4
  210. Segment(W_4, Z_4) → f_4
  211. Mirror(U_4, f_4) → A_5
  212. Mirror(V_4, f_4) → B_5
  213. Segment(A_5, B_5) → g_4
  214. Mirror(W_4, g_4) → C_5
  215. Mirror(Z_4, g_4) → D_5
  216. Segment(C_5, D_5) → h_4
  217. Mirror(A_5, h_4) → E_5
  218. Mirror(B_5, h_4) → F_5
  219. Segment(E_5, F_5) → i_4
  220. Mirror(C_5, i_4) → G_5
  221. Mirror(D_5, i_4) → H_5
  222. Segment(G_5, H_5) → j_4
  223. Mirror(E_5, j_4) → I_5
  224. Mirror(F_5, j_4) → J_5
  225. Segment(I_5, J_5) → k_4
  226. Mirror(G_5, k_4) → K_5
  227. Mirror(H_5, k_4) → L_5
  228. Segment(K_5, L_5) → l_4
  229. Point(a_4) → M_5
  230. Point(b_4) → N_5
  231. Point(c_4) → O_5
  232. Point(d_4) → P_5
  233. Point(e_4) → Q_5
  234. Point(f_4) → R_5
  235. Point(g_4) → S_5
  236. Point(h_4) → T_5
  237. Point(i_4) → U_5
  238. Point(j_4) → V_5
  239. Point(k_4) → W_5
  240. Point(l_4) → Z_5
  241. Vector(A_6, B_6) → u
  242. Vector(B_6, C_6) → u_4
  243. Vector(C_6, D_6) → v_4
  244. Vector(D_6, E_6) → w_4
  245. Vector(E_6, F_6) → m_4
  246. Vector(F_6, G_6) → n_4
  247. Vector(G_6, H_6) → p_4
  248. Vector(H_6, I_6) → q_4
  249. Vector(I_6, J_6) → r_4
  250. Vector(J_6, K_6) → s_4
  251. Vector(K_6, L_6) → t_4
  252. Vector(L_6, M_6) → u_5
  253. Vector(M_6, N_6) → v_5
  254. Vector(N_6, O_6) → w_5
  255. Vector(O_6, P_6) → a_5
  256. Vector(P_6, Q_6) → b_5
  257. Vector(Q_6, R_6) → c_5
  258. Segment(F, V) → d_5
  259. Vector(S_6, T_6) → e_5

AI Drawing Prompt Reference

Create multiple points on the horizontal axis and select one on the non-negative half-axis. Connect this point to two adjacent points on the axis to form line segments. Mirror each segment and calculate midpoints, midpoints of midpoints, etc., to form a series of points. Draw circles centered at one point with radii of 0.5 and centered at other midpoints. Finally, connect specific points to form paths, demonstrating multi-path characteristics through geometric reflections.
The prompt above was compiled from the original drawing commands and is for reference only.